The advanced gas-cooled reactor (AGR) was developed in the United Kingdom (UK) as a successor to the Magnox gas-cooled reactor. (See Magnox Power Station.) As the aim was to operate at higher fuel, cladding and gas temperatures, it was necessary to change both material and design. In the initial design stage uranium was to be replaced by uranium oxide ceramic fuel and magnox cladding be beryllium. Later, because of developmental problems and the reduction in the price of enriched U O2, the cladding selected was stainless steel, its additional neutron absorption being offset by higher enrichment. The lower thermal conductivity of U O2 necessitated smaller diameter fuel in order to keep center fuel temperature down. The introduction of hollow fuel pellets also helped to limit temperature and had the additional advantage of accommodating released fission gases without unduly increasing internal gas pressure. The small diameter fuel was arranged in a cluster of fuel pins in each coolant channel in order to generate the required power.
The first AGR to be built was the pilot reactor, WAGR, designed by the UK Atomic Energy Authority and built on their site at Windscale, Sellafield, Cumbria. Research and development progressed in parallel with the design work on many aspects, including heat transfer. Heat transfer enhancement was achieved by means of small height discrete roughening of the cladding, as a means of disturbing the boundary layer. This led to the development of an isolated square-rib form of roughness, which offered advantages over other forms such as screw threads, sine waves and studs, in terms of economy in steel, relative ease of manufacture and thermal performance. Thus, the original idea of 36 smooth beryllium cans came to be replaced by 21 roughened stainless steel cans of larger diameter. (See Augmentation of Heat Transfer, Single-Phase Systems.)
By the time the commercial AGR (CAGR) was being designed (in the early stages of operation of WAGR), research work had shown that the optimum rib pitch to height ratio was about 7 with another optimum at about 2.5. The former was preferred because of its much lower steel content. The value of 7.2 specified in manufacture was arrived at by averaging manufacturing tolerances on pitch and height.
When this optimum roughness, which had a rib height of 0.011 inches (and hence a ratio of rib height to hydraulic equivalent diameter of only 0.007), was chosen it meant that WAGR ѕ a test bed for CAGR ѕ had to opt for a new pin design. The first arrangement, with 12 of the larger pins on an approximately square array with the 8 outer pins located very close to the channel wall, was made without involving heat transfer expertise and resulted in overheating and pin failure. It was soon replaced by a single-ring, nine-pin design in an annular passage formed between the graphite channel and an inner graphite cylinder. It is this design, based like the earlier 21-pin design on computer prediction using the HOTSPOT code developed at the Windscale heat transfer laboratories, that provided the bulk of irradiation experience for CAGR. In-pile measurement and out-of-pile fuel element examination, backed up by research, provided information on pin bowing and its causes; material properties; fission gas release; graphite deposition (arising from the chemical reactions between the graphite and the carbon dioxide coolant, enhanced by radiation); oxidation; fuel pin failure; and heat transfer and fluid flow. The reactor was instrumented to provide measurements of channel flow rate, inlet and outlet gas temperatures and can temperatures.
The roughening on the can was first produced by machining, later by grinding. The meter-long cans were ground down from thick tube stock in two stages, using a half-meter-long grinding wheel containing slots at the specified rib pitch and width. Hundreds of pins could be ground before the wheel wore down, ensuring good repeatability between pins with regard to rib pitch. A quicker and cheaper method, called thread-whirling, was later developed. It produced a single-start spiral at an angle of 2.5° to the transverse direction. Tests showed that the angle had a negligible effect on performance. A further development of the rib design was the multi-start rib (see Wilkie, 1966) manufactured by a process akin to thread whirling.
The UK CAGRs, namely Dungeness B, Hinkley Point B, Hunterston B, Heysham, Hartlepool and Torness, all use 36-pin clusters formed by three rings of six, twelve and eighteen roughened pins with a central smooth tie tube all contained within a machined graphite sleeve forming the coolant flow passage. Eight of these meter-long elements are stacked vertically in a reactor channel. Although the fuel element assemblies can be aligned before loading so that like pins in neighboring assemblies are in line, the elements are free to turn and indeed do turn, especially during on-power loading. Less than 5° rotation is sufficient to cause increases in pressure drop and in temperature variations around the pins, as a result of the flow from a lower assembly meeting the blunt pin ends of the next assembly. These effects are taken into account when assessing operating conditions.
The initial fuel employed single-start ribs. For some replacement fuel 12 start multi-start ribs 0.163 in high, with a pitch to height ratio of 6.5 and a lead angle of 34°, have been adopted to promote coolant mixing. The Reynolds number is in the region of 106 [Wilkie and Mantle (1979)].
Refuelling can take place off-load or on-load; the latter became possible after the machining of ribs onto the outer surface of the graphite sleeve [Wilkie et al. (1989)].
Prior to adoption of roughened surfaces in AGRs, it had been maintained that roughening introduced a penalty in performance in that Friction Factor, f, was increased much more than Nusselt Number, Nu, or Stanton Number, St, and therefore was only of value in specific situations where pressure drop was unimportant or small size essential. What had not been realized was that while keeping coolant mass flow rate and temperature rise fixed, the pumping power could be reduced for the same thermal performance by increasing the flow area ѕ provided that St3/f is improved by roughening [Walker and Wilkie (1967)]. Also, the thermal performance could be improved for the same pumping power by increasing the flow area if St/f1/3 is improved by roughening [Wilkie (1971)]. Variations of these criteria, when parasitic pressure losses caused by support features were taken into account, are also given. The ribbed surfaces chosen for CAGR give a Stanton number about 2.5 times higher than a smooth surface and a friction factor about 7 times higher at the reactor Reynolds number. This is equivalent to an increase in thermal performance St/f1/3 of some 40%. The data for a wide variety of ribbed surfaces is contained in Wilkie, 1966a.
The multi-start ribbed design, first conceived in 1965 (see Wilkie, 1966a, for friction factor data), produced a marked reduction in friction factor compared with a transverse ribbed design, with a concomitant reduction in Stanton number. Several designs gave improved thermal performance [White and Wilkie (1970)].
In all AGRs, there are flow passages with a mixture of boundary conditions. For example, the flow between the outer facing surfaces of the outer ring of pins is bounded by a roughened surface on the pins and a smooth surface, or rather a slightly roughened machined surface, on the inner surface of the graphite sleeve. A similar situation applied between the inner facing surfaces of the inner pins and the tie tube, and between the ribbed outer surface of the graphite sleeve and the “smooth” graphite moderator block. Similarly, because of decreasing neutron absorption from the outer pins to the inner pins and the slowing down of neutrons by the graphite, all pin surfaces and all graphite surfaces are subject to different heat fluxes. These vary laterally, circumferentially and longitudinally throughout the reactor core. Little information has been available on these effects and a solution had to be found.
The seminal contribution was made by Hall in 1958, who developed the idea of dividing the annular flow zone into two parts, separated by the surface of zero shear stress taken to be located at the peak of the velocity profile in the annulus. The coolant temperature distribution, which had zero gradient at the adiabatic insulated unheated channel wall, was transformed to provide a profile with the same temperature at the heated roughened wall, but with zero gradient at the proposed zero shear stress surface. The Stanton number, friction factor and Reynolds number ѕ all based on a hydraulic equivalent diameter defined by the perimeter of the roughened cylinder and the flow area between the roughened cylinder and the zero shear stress surface ѕ were the basic data defining the performance of the roughened surfaces tested [Wilkie (1966a)].
The labor of measuring velocity and temperature profiles for all future tests was reduced by correlating the data to provide the position of the zero shear stress surface in terms of more easily measured quantities. A calculation procedure was then laid down [Wilkie (1966a)]. This procedure was more accurate than the Hall transformation since it was free of the random experimental error attached to the measurements.
However, it became clear that the large apparent increase in the smooth outer wall friction factor, as the inner wall friction factor increased (K3 factor), presented a gap in understanding. Further study [Wilkie et al. (1963)] of friction factor with a large aspect ratio rectangular channel, the walls of which could be made identical or non-identical in degree of roughening, suggested that one explanation for the large increase in smooth friction factor was the noncoincidence of the maximum velocity and the zero shear stress surfaces. This was later confirmed by direct measurement [Kjellstrom (1965)]. Warburton and Pirie, 1973, later amended the K3 factor to a lower but nonzero value so that the transformation calculation implicitly used the correct zero shear stress surface.
The transformation procedure, in effect, permits data to be applied to a fully roughened and fully heated passage, e.g., a circular pipe, although there are effects of passage shape, defined by the ratio of roughened cylinder radius to zero-shear surface radius for convex surfaces [Rapier (1963-4)].
Instead of correlating Stanton number and friction factor in terms of the several dimensionless groups required to define a roughened surface (e.g., pitch to height), a more general correlation involving roughness and passage shape parameters has been devised [Firth (1979) and Dawson et al. (1983)].
In applying the data to passages with nonuniform boundary conditions, a reverse of the transformation procedure is required [Wilkie and White (1965) and Rapier (1963-4)]. This, together with the roughness correlations for the Stanton number and friction factor, the treatment of turbulent mixing of heat, conduction in the fuel and can and thermal radiation between surfaces is embodied in the computer code HOTSPOT devised by Rapier (for initial version see Cowking, 1970).
Cowking, C. B. (1970) HOTSPOT ѕ An IBM computer programme for calculation of systematic can and fuel temperatures in gas-cooled rod-cluster fuel channel. UK Atomic Energy Authority TRG Report 1961 (R).
Dawson, J. T., Firth, R. J., Langley, M. J., Jackson, G. F., Rapier, A. C., and Wilkie, D. (1983) A comparison of measured and predicted can temperatures in simulated CAGR fuel elements. Paper 144, Br. Nucl. Energy Soc. Conf. “Gas-cooled Reactors Today”, London.
Firth, R. J. (1979) A method for analysing heat transfer and pressure drop data from partially roughened annular channels. UK Atomic Energy Authority TRG Report ND-R-301 (W).
Hall, W. B. (1958) Heat transfer in channels having rough and smooth surfaces. UK AEA Report ICR-TN/W832. Also J. Mech. Eng. Sci. (1962), Vol. 4, 287.
Kjellstrom, M. B. and Hedberg, S. (1965) On shear stress distributions for flow in smooth or partially rough annuli. AE-RTL-796.
Rapier, A. C. (1963-4) Forced convection heat transfer in passages with varying roughness and heat flux around the perimeter. Thermodyn. and Fluid Mech. Convection, Cambridge, Proc. Instn. Mech. Engrs., Vol. 178, Pt. 31, 12-20.
Walker, V. and Wilkie, D. (1967) The wider application of roughened heat transfer surfaces as developed for advanced gas-cooled reactors. Symposium on High Pressure Gas as a Heat Transfer Medium. London 9-10 March, I. Mech. E.
Warburton, C. and Pirie, M. A. (1973) An improved method for analysing heat transfer and pressure drop tests on roughened rods in smooth channels. Central Electricity Generating Board, Berkeley. Report RD/B/N2621.
White, L. and Wilkie, D. (1967) The heat transfer and pressure loss characteristics of some multi-start ribbed surfaces. UKAEA TRG Report 1504 (W) Also “Augmentation of convective heat and mass transfer”. American Society of Mechanical Engineers, New York, 1970, Dec. 55-62.
Wilkie, D. (1966a) Forced convection heat transfer from surfaces roughened by transverse ribs. Third Int. Heat Transfer Conf. Chicago. Amer. Inst. Chem. E., New York Aug. Paper No. 1, pp. 1-19. Also see UKAEA TRG Report 781 (w), 1966.
Wilkie, D. (1966b) Calculation of heat transfer and flow resistance of rough and smooth surfaces contained in a single passage. Third Int. Heat Transfer Conf. Chicago. Amer. Inst. Chem. E. New York Aug. Paper No. 2, pp. 20-31.
Wilkie, D. (1971) Criteria for choice of surface for gas-cooled reactors. Nuc. Eng. Int., Vol. 16, March, No. 177, 215-217.
Wilkie, D., Parkin, M. W., and Goldthorp, R. H. (1989) UK Patent No. GB 2168192 B.
Wilkie. D., Cowin, M., Burnett, P., and Burgoyne, T. (1963) Friction factor measurements in a rectangular channel with walls of identical and non-identical roughness. UKAEA TRG Report 519 (w). Also Int. J. Heat Mass Transfer 1967, Vol. 10, May, 611-621. DOI: 10.1016/0017-9310(67)90108-1
Wilkie, D. and Mantle, P. L. (1979) Multi-start helically-ribbed fuel pins for CAGR, Nucl. Energy, Vol. 18. Aug., No. 4, 277-282.
Wilkie, D. and White, L. (1965) Calculation of flow resistance of passages bounded by a combination of rough and smooth surfaces. UKAEA TRG Report 113 (w). Also J. BNES (January 1967), 48-62.